Superlinear Scaling for Innovation in Cities

Superlinear scaling in cities, which appears in sociological quantities such as economic productivity and creative output relative to urban population size, has been observed but not been given a satisfactory theoretical explanation. Here we provide a network model for the superlinear relationship between population size and innovation found in cities, with a reasonable range for the exponent.Comment: 5 pages, 5 figures, 1 table, submitted to Phys. Rev. E; references corrected; figures corrected, references and brief discussion adde

Inequality reversal: effects of the savings propensity and correlated returns

In the last decade, a large body of literature has been developed to explain the universal features of inequality in terms of income and wealth. By now, it is established that the distributions of income and wealth in various economies show a number of statistical regularities. There are several models to explain such static features of inequality in an unifying framework and the kinetic exchange models, in particular, provide one such framework. Here we focus on the dynamic features of inequality. In the process of development and growth, inequality in an economy in terms of income and wealth follows a particular pattern of rising in the initial stage followed by an eventual fall. This inverted U-shaped curve is known as the Kuznets Curve. We examine the possibilities of such behavior of an economy in the context of a generalized kinetic exchange model. It is shown that under some specific conditions, our model economy indeed shows inequality reversal.Comment: 15 pages, 5 figure

On neoclassical impurity transport in stellarator geometry

The impurity dynamics in stellarators has become an issue of moderate concern due to the inherent tendency of the impurities to accumulate in the core when the neoclassical ambipolar radial electric field points radially inwards (ion root regime). This accumulation can lead to collapse of the plasma due to radiative losses, and thus limit high performance plasma discharges in non-axisymmetric devices.\\ A quantitative description of the neoclassical impurity transport is complicated by the breakdown of the assumption of small $\mathbf{E}\times \mathbf{B}$ drift and trapping due to the electrostatic potential variation on a flux surface $\tilde{\Phi}$ compared to those due to the magnetic field gradient. The present work examines the impact of this potential variation on neoclassical impurity transport in the Large Helical Device (LHD) stellarator. It shows that the neoclassical impurity transport can be strongly affected by $\tilde{\Phi}$. The central numerical tool used is the $\delta f$ particle in cell (PIC) Monte Carlo code EUTERPE. The $\tilde{\Phi}$ used in the calculations is provided by the neoclassical code GSRAKE. The possibility of obtaining a more general $\tilde{\Phi}$ self-consistently with EUTERPE is also addressed and a preliminary calculation is presented.Comment: 11 pages, 15 figures, presented at Joint Varenna-Lausanne International Workshop on Theory of Fusion Plasmas, 2012. Accepted for publication to Plasma Phys. and Control. Fusio

Pareto versus lognormal: a maximum entropy test

It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one to identify the true data-generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units

The terrestrial evolution of metabolism and life – by the numbers

<p>Abstract</p> <p>Background</p> <p>Allometric scaling relating body mass to metabolic rate by an exponent of the former (<it>Kleiber's Law</it>), commonly known as quarter-power scaling (QPS), is controversial for claims made on its behalf, especially that of its universality for all life. As originally formulated, Kleiber was based upon the study of heat; metabolic rate is quantified in watts (or calories per unit time). Techniques and technology for metabolic energy measurement have been refined but the math has not. QPS is susceptible to increasing deviations from theoretical predictions to data, suggesting that there is no single, universal exponent relevant to all of life. QPS's major proponents continue to fail to make good on hints of the power of the equation for understanding aging.</p> <p>Essentialist-deductivist view</p> <p>If the equation includes a term for efficiency in the exponent, thereby ruling out thermogenesis as part of metabolism, its heuristic power is greatly amplified, and testable deductive inferences are generated. If metabolic rate is measured in watts and metabolic efficiency is a redox-coupling ratio, then the equation is essentially about the energy storage capacity of organic molecules. The equation is entirely about the essentials of all life: water, salt, organic molecules, and energy. The water and salt provide an electrochemical salt bridge for the transmission of energy into and through the organic components. The equation, when graphed, treats the organic structure as battery-like, and relates its recharge rate and electrical properties to its longevity.</p> <p>Conclusion</p> <p>The equation models the longevity-extending effects of caloric restriction, and shows where those effects wane. It models the immortality of some types of cells, and supports the argument for the origin of life being at submarine volcanic vents and black smokers. It clarifies how early life had to change to survive drifting to the surface, and what drove mutations in its ascent. It does not deal with cause and effect; it deals with variables in the essentials of all life, and treats life as an epiphenomenon of those variables. The equation describes how battery discharge into the body can increase muscle mass, promote fitness, and extend life span, among other issues.</p

Synthetic Mirnov diagnostic for the validation of experimental observations

A synthetic Mirnov diagnostic has been developed to investigate the capabilities and limitations of an arrangement of Mirnov coils in terms of a mode analysis. Eight test cases have been developed, with different coil arrangements and magnetic field configurations. Three of those cases are experimental configurations of the stellarator Wendelstein 7-X. It is observed that, for a high triangularity of the flux surfaces, the arrangement of the coils plays a significant role in the exact determination of the poloidal mode number. For the mode analysis, torus and magnetic coordinates have been used. In most cases, the reconstruction of the poloidal mode number of a prescribed mode was found to be more accurate in magnetic coordinates. As an application, the signal of an Alfvén eigenmode, which has been calculated with a three-dimensional magnetohydrodynamics code, is compared to experimental observations at Wendelstein 7-X. For the chosen example, the calculated and measured mode spectra agree very well and additional information on the toroidal mode number and localization of the mode has been inferred

Broadband Alfvénic excitation correlated to turbulence level in the Wendelstein 7-X stellarator plasmas

During the first operational phase (OP1) of the Wendelstein 7-X (W7-X) stellarator, poloidal magnetic field fluctuations, $\dot{B}_{\theta}$, were measured in several different plasma scenarios with a system of Mirnov coils. In the spectrograms, multiple frequency bands close together in frequency are observed below f = 600 kHz. Furthermore, a dominant feature is the appearance of a frequency band with the highest spectral amplitude centred between $f = 180-220$ kHz. The fluctuations are observed from the beginning of most W7-X plasmas of OP1, which were often operated solely with electron cyclotron resonance heating. The fluctuations show characteristics known from Alfvén waves and possibly Alfvén eigenmodes (AEs). However, the fast particle drive from heating sources, which is generally a driver necessary for the appearance of AEs in magnetic confinement plasmas, is absent in most of the analysed experiments. A characterization of the Alfvénic fluctuations measured during OP1 plasmas is possible using a newly developed tracking algorithm. In this paper, we extensively survey the different spectral properties of the fluctuations in correlation with plasma parameters and discuss possible driving mechanisms. The correlation studies of the dynamics of the possible ellipticity induced AEs indicate that Alfvén activity in the frequency interval between $f = 100-450$ kHz could be excited due to an interaction with turbulence, or profile effects also affecting the turbulence amplitude

Spin density wave dislocation in chromium probed by coherent x-ray diffraction

We report on the study of a magnetic dislocation in pure chromium. Coherent x-ray diffraction profiles obtained on the incommensurate Spin Density Wave (SDW) reflection are consistent with the presence of a dislocation of the magnetic order, embedded at a few micrometers from the surface of the sample. Beyond the specific case of magnetic dislocations in chromium, this work may open up a new method for the study of magnetic defects embedded in the bulk.Comment: 8 pages, 7 figure